Magnetic trap for cylindrical diamagnetic materials

ABSTRACT

A method for self-aligning diamagnetic materials includes contacting first and second magnets together other along a contact line so as to generate a diametric magnetization that is perpendicular to the contact line. A diamagnetic rod is positioned with respect to the first and second magnets to levitate above the contact line of the first and second magnets.

DOMESTIC PRIORITY

This application is a continuation of U.S. patent application Ser. No.14/743,051, filed Jun. 18, 2015, which is a continuation of U.S. patentapplication Ser. No. 14/537,060, filed Nov. 10, 2014, which is acontinuation-in-part of U.S. patent application Ser. No. 13/969,333,filed Aug. 16, 2013, now U.S. Pat. No. 8,895,355, which is acontinuation of U.S. patent application Ser. No. 13/800,918, filed Mar.13, 2013, now U.S. Pat. No. 9,093,377, the disclosures of which areincorporated by reference herein in their entireties.

BACKGROUND

Embodiments of the invention relate generally to trapping cylindricaldiamagnetic materials and, in particular, to positioning diamagneticmaterials in a contactless manner by magnets.

Miniaturization of semiconductor circuits has led to the fabrication oftransistor devices on a smaller and smaller scale. At the end of scalingtechnology is a quasi one-dimensional structure, such as semiconductornanowires or carbon nanotubes. Semiconductor nanowires can be fabricatedusing traditional lithography technology. However they are prohibitivelyexpensive as the device scale becomes very small, such as less than fivenanometers (nm) in diameter. In some applications, semiconductor wiresor carbon nanotubes are synthesized using various processes, such aschemical vapor deposition (CVD), which wires or nanotubes can beharvested and subsequently fabricated to serve as a semiconductordevice.

One of the key challenges in utilizing semiconductor wires or carbonnanotubes is to assemble them in large amounts and in precise locationson a substrate to serve as an integrated circuit with a method suitablefor large scale manufacturing.

SUMMARY

According to one embodiment of the invention, a system for self-aligningdiamagnetic materials includes first and second magnets contacting eachother along a contact line and having a diametric magnetizationperpendicular to the contact line and a diamagnetic rod positioned tolevitate above the contact line of the first and second magnets.

According to another embodiment of the invention, a method of arranginga diamagnetic rod includes levitating a diamagnetic rod above a contactline at which a first magnet contacts a second magnet, the first magnetand the second magnet having diametric magnetization in a directionperpendicular to the contact line.

Additional features and advantages are realized through the techniquesof the present invention. Other embodiments and aspects of the inventionare described in detail. For a better understanding of embodiments ofthe invention, refer to the description and to the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

Features characterizing embodiments of the present invention aredescribed in the specification and claims which follow. These features,and advantages of embodiments of the invention are apparent from thefollowing detailed description taken in conjunction with theaccompanying drawings in which:

FIG. 1 illustrates a magnetic trap and a graph of potential energy ofthe magnetic trap according to an embodiment of the invention;

FIG. 2A is a cross-sectional view of a magnetic trap according to oneembodiment of the invention;

FIG. 2B is a cross-sectional view of a magnetic trap according toanother embodiment of the invention;

FIG. 3 illustrates a vertical confinement potential of the magnetic trapaccording to one embodiment;

FIG. 4A illustrates one magnet of a magnetic trap according to oneembodiment;

FIG. 4B illustrates a graph of a longitudinal potential of a magnetictrap according to one embodiment;

FIG. 5A illustrates one view of deposition of diamagnetic materials on amagnetic trap array according to an embodiment of the invention;

FIG. 5B illustrates another view of deposition of diamagnetic materialson a magnetic trap array according to an embodiment of the invention;

FIG. 5C illustrates one view of cleaning non-captured diamagneticmaterials from a magnetic trap array according to one embodiment;

FIG. 5D illustrates another view of cleaning non-captured diamagneticmaterials from a magnetic trap array according to one embodiment;

FIG. 6A illustrates a first stage of transferring diamagnetic materialsto a target substrate according to one embodiment;

FIG. 6B illustrates a second stage of transferring diamagnetic materialsto a target substrate according to one embodiment;

FIG. 7 illustrates diamagnetic rods transferred to a target substrate;and

FIG. 8 is a flowchart illustrating a method according to an embodimentof the invention.

DETAILED DESCRIPTION

Conventional systems and methods have difficulty assembling largenumbers of carbon nanotubes or semiconductor wires to form integratedcircuits. Carbon nanotubes and most semiconductors are diamagnetic, withmagnetic susceptibility χ<0. Embodiments of the invention relate tosuspension of diamagnetic rods by diametrically magnetized magnets(magnetic polarization along the diameter of the magnet) to align thediamagnetic rods.

FIG. 1A illustrates a magnetic trap 100 according to an embodiment ofthe invention. FIG. 1B illustrates potential energy that traps thediamagnetic material 103 in the magnetic trap 100. The magnetic trap 100includes a first magnet 101 and a second magnet 102. A diamagnetic rod103 or cylinder is positioned above a contact line where the firstmagnet 101 contacts the second magnet 102. As illustrated in FIG. 2A,the first magnet 101 and the second magnet 102 are diametricallymagnetized with volume magnetization M in a width direction x andcontact each other at the contact line 104. Because of the finite lengthof the magnets 101 and 102, i.e. because each of the magnets 101 and 102has a flat face at each end, the magnets 101 and 102 produce alongitudinal potential U(z) that traps the diamagnetic rod 103 along thelongitudinal direction (z) that has a form of “camel-back” potential.

In embodiments of the invention, the diamagnetic rod 103 is trapped insuch a way that the rod 103 levitates above the contact line 104 in avertical direction y, and maintains its location in each of alongitudinal direction z and a lateral or width direction x. Inaddition, in embodiments of the invention, the first and second magnets101 and 102 have a uniform shape along the longitudinal direction z. Inother words, if the first and second magnets 101 and 102 have acylindrical shape as illustrated in FIG. 1, then a diameter of thecylinder is uniform along the longitudinal direction z. Similarly, in anembodiment in which the first and second magnets 201 and 202 have adiamond cross-section shape, as illustrated in FIG. 2B, the angles andsides of the first and second magnets 201 and 202 are uniform along thelongitudinal direction z. While a circular cross-section shape isillustrated in FIGS. 1A and 2A, and a diamond cross-sectional shape isillustrated in FIG. 2B, embodiments of the invention encompass anycross-sectional shape, as long as the first and second magnets 101 and102 have a uniform shape along the longitudinal direction z.

In embodiments of the invention, the longitudinal direction zcorresponds to a length axis of the diamagnetic rod 103, an origin axis,center length axis or center-of-gravity axis of the first and secondmagnets 101 and 102 and the contact line 104 where the first magnet 101contacts the second magnet 102. The first and second magnets 101 and 102are magnetized diametrically, parallel to the lateral or width axis xand perpendicular to the longitudinal axis z.

FIGS. 3A and 3B illustrate a magnetic trap 100 and vertical confinementpotential of the magnetic trap 100.

The trapping potential in the vertical direction in the magnetic trapsystem with cylindrical magnets is given as:

$\begin{matrix}{{U_{y}(y)} = {\pi\; b^{2}{l\left( {{\rho_{R}g\; y} - {2\frac{\chi}{\chi + 2}\mu_{0}M^{2}\frac{\left( {1 - \eta^{2}} \right)^{2}}{\left( {1 + \eta^{2}} \right)^{2}}}} \right)}}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

where b is the radius of the rod, l is the length of the rod, ρ_(R) isthe mass density of the rod, χ is the magnetic susceptibility of therod, g is the gravitational acceleration, μ₀ is the magneticpermeability in vacuum, M is the volume magnetization of the magnets andη=y/a, where y is the vertical position of the rod and a is the radiusof the magnet.

The equilibrium point y_(EQ) where the rod is trapped or levitates canbe obtained by solving for η_(EQ) using:

$\begin{matrix}{{{\rho_{R}{ga}} + {8\mu_{0}M^{2}\frac{\chi}{\chi + 2}\frac{{\eta_{EQ}\left( {3 - \eta_{EQ}^{2}} \right)}\left( {1 - \eta_{EQ}^{2}} \right)}{\left( {1 + \eta_{EQ}^{2}} \right)^{5}}}} = 0} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

FIG. 4A illustrates one magnet 101 of a magnetic trap 100 to trap adiamagnetic rod 103 according to one embodiment. One magnet 101 isillustrated, while a contacting magnet (such as magnet 102) is omittedfrom FIG. 4A, for purposes of description only. FIG. 4B is a graph of alongitudinal potential of a magnetic trap according to embodiments ofthe invention.

The longitudinal potential is given as:

$\begin{matrix}{{U(z)} = {\pi\; b^{2}{l\left( {{\rho_{R}g\; y_{EQ}} - {\frac{2}{\mu_{0}}\frac{\chi}{\chi + 2}{B_{tot}(z)}^{2}}} \right)}}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

where B_(tot)(z)=B₁(z)+B₂(z) is the magnetic field on the rod usingdipole line model approximation, which only has x component with:

                                     (Equation  4)${B_{1}(z)} = {{- \frac{\mu_{0}{Ma}^{2}}{2\left( {y_{EQ}^{2} + a^{2}} \right)}}\left( {\frac{{L/2} - z}{\sqrt{\left( {{L/2} - z} \right)^{2} + y_{EQ}^{2} + a^{2}}} + \frac{{L/2} + z}{\sqrt{\left( {{L/2} + z} \right)^{2} + y_{EQ}^{2} + a^{2}}}} \right)\hat{x}}$     and,                                     (Equation  5)${B_{2}(z)} = {\frac{\mu_{0}{Ma}^{4}}{2\left( {y_{EQ}^{2} + a^{2}} \right)^{2}}\left( {\frac{{3\left( {y_{EQ}^{2} + a^{2}} \right)\left( {{L/2} + z} \right)} + {2\left( {{L/2} + z} \right)^{3}}}{\left\lbrack {\left( {{L/2} - z} \right)^{2} + y_{EQ}^{2} + a^{2}} \right\rbrack^{3/2}} + \frac{{3\left( {y_{EQ}^{2} + a^{2}} \right)\left( {{L/2} - z} \right)} + {2\left( {{L/2} - z} \right)^{3}}}{\left\lbrack {\left( {{L/2} - z} \right)^{2} + y_{EQ}^{2} + a^{2}} \right\rbrack^{3/2}}} \right)\hat{x}}$

where L is the length of the magnet and {circumflex over (x)} is theunit vector along x direction. This longitudinal potential has a form of“camel-back potential” which creates a confinement with a minimum pointat the center and two peaks at both ends as shown in FIG. 4B.Accordingly, the diamagnetic rod 103 is trapped in the center of themagnetic trap 100 in a longitudinal direction z.

According to another embodiment, the longitudinal potential may bedetermined as:

${U_{T}\left( {0,y_{EQ},z} \right)} = {\pi\; b^{2}{l\left( {{\rho_{R}g\; y_{EQ}} - {\frac{2}{\mu_{0}}\frac{\chi}{\chi + 2}{B_{T}^{2}\left( {0,y_{EQ},z} \right)}}} \right)}}$

Where, B_(T)(0, y, z) is the total magnetic field on the rod at thecenter of the trap (x=0). Due to system symmetry, the magnetic fieldonly has x component. This magnetic field is given as:B _(T)(y,z)=B _(M)(a,y,z)+B _(M)(−a,y,z)

where B_(M) is the magnetic field due to a single cylindrical diametricmagnet centered at origin given as:

${B_{M}\left( {x,y,z} \right)} = {\frac{\mu_{0}{Ma}}{4\pi}{\int_{0}^{2\pi}{\sum\limits_{{n = 1},2}{{\frac{\left( {- 1} \right)^{n}}{u_{n}^{2} + s^{2} + {u_{n}\sqrt{u_{n}^{2} + s^{2}}}}\left\lbrack {{x - {a\;\cos\;\phi}},{y\  - {a\;\sin\;\phi}},{u_{n} + \sqrt{u_{n}^{2} + s^{2}}}} \right\rbrack}\cos\;\phi{\mathbb{d}\phi}}}}}$

where, L is the length of the magnet, s²=(x−a cos φ)²+(y−a sin φ)² andu_(1,2)=z±L/2. As described above, the longitudinal potential has a formof “camel-back potential” which creates a confinement with a minimumpoint at the center and two peaks at both ends as shown in FIG. 4B.Accordingly, the diamagnetic rod 103 is trapped in the center of themagnetic trap 100 in a longitudinal direction z.

The shape of the camel-back potential determines a length of adiamagnetic rod 103 that may be trapped, since only a diamagnetic rod103 with a length of less then around eighty percent (80%) but more thanten percent (10%) of the length L of the magnets 101 and 102 could betrapped in stable condition in the magnetic trap 100. Accordingly, inembodiments of the invention, the length L of the magnets 101 and 102may be selected to filter the length of diamagnetic rods that a user orsystem desires to trap. The three dimensional confinement in themagnetic trap 100 is exploited to trap and self assemble semiconductorstructures which are mostly diamagnetic materials.

This system can also be utilized to measure the magnetic susceptibilityof the rod (χ), which is a parameter that that is difficult to measureusing other techniques especially for a very small particle. Themagnetic susceptibility of a diamagnet has a value of χ<0, while amagnetic susceptibility of a ferromagnet material has a value of χ>0.The camel back potential of the system gives rise to an oscillation forthe rod along the longitudinal (z) direction with a period T. Thisinformation can be used to extract the magnetic susceptibility (χ) ofthe rod using the following approximation:

$\begin{matrix}{\chi = {- \frac{2}{1 + {439\;\mu_{0}M^{2}{T/2}\pi^{2}\rho_{R}}}}} & \left( {{Equation}\mspace{14mu} 6} \right)\end{matrix}$

According to another embodiment, the magnetic susceptibility of the rodmay be determined using a more exact expression as:

$\chi = {- \frac{2}{1 + {\alpha\;\mu_{0}M^{2}{T/4}\pi^{2}\rho_{R}L^{2}}}}$where α is a dimensionless geometric parameter defined as:α=2L ²/μ₀ ² M ²×∂² B _(T) ²(0,y _(EQ),0)/∂z ²

FIGS. 5A to 7 illustrate a process for positioning diamagnetic rods on asubstrate according to one embodiment of the invention. FIG. 8illustrates a flowchart of a method according to an embodiment of theinvention. FIGS. 5A and 5B illustrate a magnetic trap assembly 500 at astage where diamagnetic rods are trapped by magnetic traps.

In block 801 of FIG. 8, diamagnetic rods 513 or wires, includingsemiconductor nanowires or carbon nanotubes may be deposited on asubstrate 501 including a plurality of magnetic traps 510 a to 510 hthat form a magnetic trap array. The magnetic traps 510 a to 510 h maybe arranged in any manner and may have any length to correspond todesired arrangements and lengths of the diamagnetic rods 513 in acircuit. The diamagnetic rods 513 may be deposited by applying asolution to the substrate 501, dipping the substrate 501 in a solutionor by any other method. Rods 513 of predetermined lengths, based on thelengths of the magnets 511 and 512 of the magnetic traps 510 a to 510 h,are trapped in the magnetic traps 510 a to 510 h, and the remaining rodsare left on a surface of the substrate 510.

In FIG. 5A, a first magnetic trap 510 a includes a first magnet 511 acontacting a second magnet 512 a, and a first diamagnetic rod 513 a istrapped by the magnetic trap 510 a. A second magnetic trap 510 bincludes a first magnet 511 b contacting a second magnet 512 b, and asecond diamagnetic rod 513 b is trapped by the magnetic trap 510 b. Thefirst and second magnetic traps 510 a and 510 b are described in detailby way of example, and each of the magnetic traps 510 c to 510 hincludes the first magnet 511 and the second magnet 512. In FIG. 5A,reference numerals 513 x, 513 y and 513 z are used to illustrate threeexamples of non-trapped diamagnetic rods 513.

As illustrated in FIG. 5B, the first and second magnets 511 and 512 ofthe magnetic traps 510 may have any cross-sectional shape, including ahouse shape, or a shape of a combined rectangle and triangle, as long asthe first and second magnets 511 and 512 have a uniform shape along alongitudinal axis corresponding to the length of the first and secondmagnets 511 and 512.

In block 802 of FIG. 8, and referring to FIGS. 5C and 5D, thenon-trapped wires 513, including the wires 513 x, 513 y and 513 z ofFIG. 5A, may be removed from the substrate 501, such as by applicationof a liquid solution to the substrate 501, by gentle agitation of thesubstrate 501 or by any other cleaning method.

In block 803 of FIG. 8, the diamagnetic materials captured in themagnetic traps 510 a to 510 h are transferred to a target substrate.Referring to FIG. 6A, a target substrate 520, may be brought intoproximity with the magnetic traps 510 and the diamagnetic rods 513. Inone embodiment, the target substrate is treated such that contact withthe diamagnetic rods 513 results in the diamagnetic rods adhering to asurface of the target substrate 520. As illustrated in FIG. 6B, thesubstrate 501 may be inverted over the target substrate 520 to apply thediamagnetic rods 513 to the target substrate 520.

In one embodiment, the diamagnetic rods 513 are carbon nanotubes wrappedin a surfactant and are selectively placed on the target substrate 520based on an ion exchange between a functional surface monolayer and thesurfactant-wrapped carbon nanotubes in an aqueous solution. Strongelectrostatic interaction between the surface monolayer and the nanotubesurfactant leads to the placement of individual nanotubes. In oneembodiment, the monolayer is formed of4-(N-hydroxycarboxamido)-1-methylpyridinium iodide (NMPI) molecules. Themonolayer may include a hydroxamic acid end group that self-assembles onmetal oxide surfaces, but not silicon dioxide (SiO₂). An anion of NMPImay be exchanged with the anionic surfactant wrapped around thenanotubes, which results in a strong coulombic attraction between anegatively charged surfactant and a positively charged monolayer.

As illustrated in FIG. 7, the diamagnetic rods 513 a to 513 h may adhereto the target substrate 520 to form wiring for an integrated circuit,for example.

Embodiments of the present invention trap diamagnetic wires or rods withmagnets or ferromagnets. The diamagnetic wires or rods may then beapplied to a substrate to form the basis for an integrated circuit.Embodiments include a system to trap and filter cylindrical diamagneticmaterials or rods including pair of magnets, such as cylindricalmagnets, block magnets, or thin film magnets. The magnets have diametricmagnetization, i.e., the magnetization is along the diameter of themagnets, perpendicular to the direction of the trapped rods. The magnetshave a finite length and flat faces on both ends to create longitudinalconfinement of the rods. The magnets are designed to capture rods ofpredetermined lengths, where only rods having a length between around10% and 80% of the magnets may be trapped.

Embodiments also include an array of magnetic traps on a substrate toform a template for self-assembly of diamagnetic materials, such assemiconductor nanowires or carbon nanotubes. Embodiments also includemethods for performing self-assembly of diamagnetic materials includingdepositing cylindrical diamagnetic materials on an array of magnetictraps, cleaning or filtering non-assembled diamagnetic materials andtransferring the captured diamagnetic materials to a substrate to formwiring for a semiconductor circuit.

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as an apparatus, system, method or computerprogram product. For example, the method of capturing diamagneticmaterials and forming wiring may be performed by a system controlled bya computer executing computer code that controls the system to executethe method. Accordingly, aspects of the present invention may take theform of an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present invention may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with an instruction execution system,apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thepresent invention may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, Smalltalk, C++ or the like and conventional proceduralprogramming languages, such as the “C” programming language or similarprogramming languages. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server. In the latterscenario, the remote computer may be connected to the user's computerthrough any type of network, including a local area network (LAN) or awide area network (WAN), or the connection may be made to an externalcomputer (for example, through the Internet using an Internet ServiceProvider).

Aspects of the present invention have been described with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products. It will be understood that eachblock of the flowchart illustrations and/or block diagrams, andcombinations of blocks in the flowchart illustrations and/or blockdiagrams, can be implemented by computer program instructions. Thesecomputer program instructions may be provided to a processor of ageneral purpose computer, special purpose computer, or otherprogrammable data processing apparatus to produce a machine, such thatthe instructions, which execute via the processor of the computer orother programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which execute on thecomputer or other programmable apparatus provide processes forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblocks may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of onemore other features, integers, steps, operations, element components,and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the disclosure in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described in order to best explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated.

While a preferred embodiment has been described, it will be understoodthat those skilled in the art, both now and in the future, may makevarious improvements and enhancements which fall within the scope of theclaims which follow.

What is claimed is:
 1. A method of arranging a diamagnetic rodcomprising: arranging first and second magnets on a substrate so as toform an array of magnetic traps defining a template for self-assemblingdiamagnetic material, each of the first and second magnets extendingalong a longitudinal direction to define a magnet length; depositing aplurality of diamagnetic rods onto the array of magnetic traps;capturing, by the array of magnetic traps, a number of captureddiamagnetic rods, among the plurality of diamagnetic rods, correspondingto a number of magnetic traps in the array of magnetic traps; levitatingthe captured diamagnetic rods in a vertical direction perpendicularabove a contact line located where the first magnet contacts the secondmagnet, the first magnet and the second magnet having a diametricmagnetization in a direction perpendicular to the contact line and thelongitudinal direction so as to generate a longitudinal energy potentialthat traps the diamagnetic rod along the longitudinal direction so as tofilter a rod length of the diamagnetic rod based on the magnet lengths,wherein the longitudinal energy potential confines the diamagnetic rodin a three-dimensional confinement within the magnetic trap andpositions the diamagnetic rod being levitated above the contact lineagainst a target substrate to form wiring on the target substrate toperform to self-assembling process, and wherein the first magnet and thesecond magnet make up one magnetic trap among an array of magnetic trapsmounted on a template substrate.
 2. The method of claim 1, furthercomprising oscillating the trapped rod along the longitudinal axis tomeasure a magnetic susceptibility of the rod.
 3. The method of claim 2,further comprising determining the magnetic susceptibility of the rodbased on a magnetic field due to a single cylindrical diametric.
 4. Themethod of claim 3, further comprising: cleaning the template substrateto remove from the template substrate any un-captured diamagnetic rodsamong the plurality of diamagnetic rods.
 5. The method of claim 4,further comprising: bringing the captured diamagnetic rods into contactwith a target substrate to form wiring on the target substrate.
 6. Themethod of claim 1, further comprising wherein the longitudinal energypotential produced having a camel-back shaped energy profile.
 7. Themethod of claim 6, wherein the camel-back shaped energy profile includesa trough region interposed between a pair of peak regions.
 8. The methodof claim 7, wherein the diamagnetic rod is levitated at approximatelythe trough portion.
 9. The method of claim 8, wherein the camel-backshaped energy profile determines that the rod length of the trappeddiamagnetic rod satisfies a length ratio with respect to the magnetlength.